This application claims Paris Convention priority of EP 02 011 929.3 filed May 29, 2002 the complete disclosure of which is hereby incorporated by reference.
The invention concerns a pulsed gradient NMR (=nuclear magnetic resonance) method using stimulated echoes for determining the translational isotropic or anisotropic diffusion coefficient of a molecule or supra-molecular assembly or the flow rate and direction of fluids containing such molecules.
A pulsed field gradient NMR method using stimulated echoes is known from A. S. Altieri, D. P. Hinton and R. A. Byrd, J. Am. Chem. Soc. 117 (1985), p. 7566-7567.
In order to determine the translational diffusion coefficient or the flow rate of a macromolecule pulsed field gradient NMR using stimulated echoes can be applied. With suitable hydrodynamic models, it is then possible to estimate the radius and the mass of the macromolecule.
However, slow diffusion coefficients D less than 10xe2x88x9210 m2/s or small flow rates, which are typically associated with biological macromolecules or supra-molecular assemblies with masses Mxe2x89xa750 kDa, are difficult to measure with this method.
This is due to the rapid longitudinal relaxation of the protons in state of the art measurements.
In methods employing stimulated echoes (STEs), the information about the localization of the molecules is temporarily stored in the form of longitudinal magnetization during a diffusion interval (i.e. a diffusion time) xcex9. Usually, the magnetization of protons is used for these experiments, since protons have a favorable gyromagnetic ratio and, of course, protons are present in effectively all macromolecules and biological materials.
However, if during the time of longitudinal relaxation of protons T1(H) no significant diffusion or flow takes place, no determination of the translational diffusion constant or the flow rate can be done. This means materials with short T1(H) values, as compared with the times necessary for significant translational diffusion or flow, are excluded from the above mentioned measurement methods of the state of the art.
One of the principal hurdles that must be overcome prior to the determination of the structures of amphiphilic membrane proteins by solution-state NMR is the optimization of the solubilization of these proteins by suitable lipids, detergents or amphiphilic polymers (xe2x80x9camphipolsxe2x80x9d). Ideally, the hydrophobic surface of the protein should be covered with the slightest possible layer of solubilizing agent, so that the overall mass of the resulting assembly remains as small as possible. If the overall mass is much larger than that of the protein itself, this translates into slow rotational diffusion, long tumbling correlation times xcfx84c, broad NMR lines, and hence poor resolution and sensitivity.
There are several approaches to the determination of the size of a supra-molecular assembly comprising a protein and its associated solubilizing agents: the kinetics of sedimentation during ultra-centrifugation, diffusion through membranes with well-defined pores, chromatography with suitable molecular sieves, neutron diffraction and pulsed-field gradient NMR. The latter method can provide a measurement of the translational diffusion coefficient D. With suitable hydrodynamic models, it is then possible to estimate the radius and hence the mass of macromolecular assemblies. Slow diffusion coefficients D less than 10xe2x88x9210 m2sxe2x88x921 associated with biological macromolecules or supra-molecular assemblies with masses Mxe2x89xa750 kDa are difficult to measure by standard pulsed-field gradient NMR methods (1-5) using stimulated echoes because of rapid longitudinal relaxation of the nuclei (usually protons) that carry the information about the localization of the molecules during the diffusion interval.
The success of the original pulsed field gradient spin-echo NMR method due to Stejskal and Tanner (1) has lead to the development of many variants, particularly methods that employ so-called stimulated echoes (STE""s) where the information about the localization of the molecules is temporarily stored in the form of longitudinal magnetization (2). Such experiments are usually carried out using the magnetization of protons, because of the favorable gyromagnetic ratio that allows one to xe2x80x98encodexe2x80x99 the initial spatial position with good accuracy without resorting to very intense gradients. Byrd and co-workers (6) have adapted a method (5) with an additional interval where the information is stored in the form of longitudinal proton magnetization to allow eddy currents to die out. More recent experiments allow one to circumvent undesirable effects of eddy currents by using so-called xe2x80x98bipolar gradientsxe2x80x99 (3). It has also been shown recently that diffusion can be distinguished from flow or convection (4). The development of novel experimental methods has been accompanied by substantial efforts to extract reliable information from the attenuation of the signals as a function of the amplitude of the gradients, which should ideally obey a Gaussian function. The rates of these decays can be estimated by various approaches using inverse Laplace transformations. This has lead to so-called DOSY (Diffusion Ordered Spectroscopy) representations (5), i.e. two-dimensional plots where the diffusion coefficients appear along the ordinates while the chemical shifts are responsible for the dispersion along the abscissas.
The storage of the information in the form of longitudinal proton magnetization is of course subject to spin-lattice relaxation T1(1H). In macromolecules such as proteins and nucleic acids, this typically limits the useful duration of the diffusion interval xcex94. In samples with masses on the order of 50 kDa, one has typically T1(1H)=30 ms so that the diffusion interval must be limited to about xcex94=30 ms (if xcex94=T1(1H), the loss in signal intensity is exp{xcex94/T1(1H)}=exe2x88x921=0.37). This limitation means that very small translational diffusion constants D are difficult to measure. In practice, conventional stimulated echo (STE) methods (6) involving proton magnetization using a 600 MHz spectrometer equipped with standard triple-axes gradients, have proven to be difficult if Dxe2x89xa610xe2x88x9210 m2sxe2x88x921. For instance, the diffusion coefficient of an aqueous solution of the protein Ubiquitin (D=2.4 10xe2x88x9210 m2sxe2x88x921 at 30xc2x0 C. for a mass of M=8 kDa) can be readily determined by the previously described method. The conventional stimulated echo method STE (6) has also been used for supra-molecular assemblies of high molecular weight (7), where it is possible to measure the diffusion coefficient of a highly mobile polyhistidine tag that has been attached to the protein and that has relatively narrow lines and slow proton spin-lattice relaxation. However, the construction of such fusion proteins is time-consuming. It can be shown that conventional STE methods are inadequate to determine the diffusion coefficient of an assembly of protein OmpA with detergent (D=10xe2x88x9210 m2sxe2x88x921 for a mass of M=50 kDa) in the absence of a polyhistidine tag.
In view of these deficiencies in prior art, it is the object of the invention to present a pulsed-field gradient NMR method that allows the determination of translational diffusion coefficients or flow rates of supra-molecular assemblies or molecules with short T1(H) values, in particular of supra-molecular assemblies or molecules with Mxe2x89xa750 kDa.
This object is achieved, according to the invention, by a pulsed field gradient method as mentioned above, characterized in that the molecule or supra-molecular assembly contains one or several isotopes (X) of non-zero nuclear spin other than protons having longitudinal relaxation times T1(X) that are longer than the longitudinal relaxation times T1(H) of the protons, and that the information about the localization of the molecule or supra-molecular assembly during the diffusion or flow interval is temporarily stored in the form of longitudinal magnetization of said isotope or isotopes.
So the standard isotope of magnetization storage, i.e. protons, is replaced by another isotope X of a different element according to the invention. Although this isotope has a lower gyromagnetic ratio and therefore provides less NMR intensity than protons, it is preferred because of a longer longitudinal relaxation time T1(X). Thus, a useful storage of localization information can be granted during a diffusion interval xcex94 that is longer than T1(H).
In a highly preferred variant of the inventive method, one of the isotopes is nitrogen-15. Nitrogen-15 can easily be enriched in most supra-molecular assemblies, since nitrogen is an abundant element in cross-linking bonds, e.g. in peptide bonds or within urethane plastics.
Alternatively or in addition, a variant of the method is characterized in that one of the isotopes is carbon-13. Carbon is present in all macromolecular assemblies or molecules, and carbon-13 can easily be enriched in case the natural content is insufficient for the intended measurement.
Also alternatively or in addition, in a variant of the method one of the isotopes is phosphorus-31. Phosphorus-31 is the only stable isotope of phosphorus, so if phosphorous is present within the supra-molecular assembly or molecule, it can readily be used for the inventive method.
In a preferred variant of the pulsed field gradient NMR method according to the invention, the molecule or supra-molecular assembly contains bio-molecules. For bio-molecules, there is a particular demand for determining their physical properties such as the translational diffusion coefficient or flow rate.
In a further development of this variant, the molecule or supra-molecular assembly comprises proteins and/or nucleic acids, solubilized by detergents or amphiphilic agents. Proteins and nucleic acids contain both nitrogen and carbon, so an investigation of the corresponding molecule or supra-molecular assembly is easy to realize with the inventive method.
A variant of the NMR method according to the invention is characterized in that subsequent to the determination of the translational diffusion coefficient the mass and radius of gyration of the molecule or supra-molecular assembly are calculated on the basis of a hydrodynamic model. Thus further physical properties of the molecule or supra-molecular assembly can be determined.
An inventive variant of the pulsed field gradient NMR method is characterized by application of a sequence of radio-frequency pulses to transfer the magnetization from protons to the said isotopes and back. This is a simple way of storing the information about the localization of the molecule or supra-molecular assembly temporarily in accordance with the invention.
A further variant of the inventive method is characterized by application of a sequence of radio-frequency pulses to convert the transverse magnetization perpendicular to the applied magnetic field of the said isotopes into longitudinal magnetization parallel to the applied magnetic field during an interval where translational diffusion or flow is monitored. This further details the storing of information about the localization of the molecule or macromolecular assembly during the diffusion interval xcex94.
Also in accordance with the invention is a variant of the method wherein the following pulse sequence is applied:
i) 90xc2x0 pulse acting on isotope X
ii) pulsed field gradient to dephase transverse magnetization
iii) selective 90xc2x0 pulse in xe2x88x92x-direction acting on resonance of isotope H of solvent
iv) 90xc2x0 pulse in x-direction acting on isotope H
v) pulsed field gradient to encode spatial position, wait delay time xcfx84
vi) simultaneously 180xc2x0 pulse in x-direction acting on isotope H and 180xc2x0 pulse in x-direction acting on isotope X
vii) pulsed field gradient to encode spatial position, wait delay time xcfx84
viii) 90xc2x0 pulse in y-direction acting on isotope H
ix) selective 90xc2x0 pulse in xe2x88x92y-direction acting on resonance of isotope H of solvent
x) pulsed field gradient to dephase transverse magnetization
xi) 90xc2x0 pulse in x-direction acting on isotope X
xii) pulsed field gradient to dephase transverse magnetization, wait delay time xcfx84
xiii) simultaneously 180xc2x0 pulse in xe2x88x92x-direction acting on isotope H and 180xc2x0 pulse in x-direction acting on isotope X
xiv) pulsed field gradient to dephase transverse magnetization, wait delay time xcfx84
xv) 90xc2x0 pulse in +x or xe2x88x92x-direction acting on isotope X
xvi) pulsed field gradient to dephase transverse magnetization
xvii) wait diffusion or flow interval xcex94
xviii) 90xc2x0 pulse in +x or xe2x88x92x-direction acting on isotope X
xix) pulsed field gradient to dephase transverse magnetization, wait delay time xcfx84
xx) simultaneously 180xc2x0 pulse in x-direction acting on isotope H and 180xc2x0 pulse in x-direction acting on isotope X
xxi) pulsed field gradient to dephase transverse magnetization, wait delay time xcfx84
xxii) selective 90xc2x0 pulse in xe2x88x92x-direction acting on resonance of isotope H of solvent
xxiii) simultaneously 90xc2x0 pulse in xe2x88x92x-direction acting on isotope H and 90xc2x0 pulse in xe2x88x92x-direction acting on isotope X
xxiv) pulsed field gradient to decode spatial position
xxv) pulsed field gradient to dephase transverse magnetization, wait delay time xcfx84
xxvi) selective 90xc2x0 pulse in x-direction acting on resonance of isotope H of solvent
xxvi) simultaneously 180xc2x0 pulse in xe2x88x92x-direction acting on isotope H and 180xc2x0 pulse in x-direction acting on isotope X
xxvii) selective 90xc2x0 pulse in x-direction acting on resonance of isotope H of solvent
xxviii) pulsed field gradient to decode spatial position
xxix) pulsed field gradient to dephase transverse magnetization, wait delay time xcfx84
xxx) acquire H signal
with xcfx84=(4JHX)xe2x88x921, and JHX being the scalar coupling constant of isotopes H and X, and xcex94 being a selectable time parameter with xcex94 greater than  greater than xcfx84. This describes one simple way to access the above-mentioned advantages of the inventive method.
Further advantages can be extracted from the description and the enclosed drawing. The features mentioned above and below can be used in accordance with the invention either individually or collectively in any combination. The embodiments mentioned are not to be understood as exhaustive enumeration but rather have exemplary character for the description of the invention.
The invention is further illustrated by means of the drawings.